Speaking as someone trained in applying the findings of modern linguistic science to teaching foreign languages and as a retired college instructor of English and ESL/EFL, I would have to say that this textbook uses a pedagogical method that makes learning the skill of READING either language extremely difficult. And I assume that most prospective students of Latin or non-modern Greek have reading as their primary goal.
If you wish to learn to read Latin well, I highly recommend the materials of Hans H. Ørberg’s Lingua Latina Per Se Illustrata. I am using them for self-study. The exercises, and, wonder of wonders, there are many of them (contrary to the paltry few sentences given in most textbooks), are outstanding from the pedagogical viewpoint of an applied linguistic scientist. Another excellent feature is that the readings form a connected discourse, telling the story of a typical Roman family. And, multas Deo gratias! there are no translation exercises. All is in Latin. A separate Latin-English glossary is available as part of the series. Although the grammar is also presented in Latin as part of the textbook lessons, there is a small book that explains the grammar in English. The presentation of the glossary and grammatical explanations in English as separate booklets instead of their inclusion in the textbook itself also helps the student to focus on learning to read Latin.
Developing translation skills (Latin to English, or even worse, English to Latin) is a waste of time for students who wish to learn to READ in Latin. Of course, if you’re preparing for an exam that requires the ability to translate, then you need to develop such skills. It is unfortunate that various educational systems still require students to translate from Latin to English and even vice-versa as part of their examination process. Who on earth does that nowadays in life outside the Academy? Very few, no doubt.
Now, with regard to learning to read in non-modern Greek (Homeric through Byzantine), I haven’t been able to find any printed materials of the quality of Hans Ørberg’s. Many texts follow the outdated pedagogical tradition of a short text (not connected discourse), a small vocabulary list, grammatical explanations, perhaps one or two exercises dealing with the declension or conjugation of pertinent parts of speech, and two translation exercises (Greek-English, English-Greek). Those I have seen have to be supplemented by exercises prepared by the instructor of the course.
I’m still looking, however. I just ordered Rouse’s Greek Boy: A Reader by W.H.D. Rouse, revised by Anne Mahoney, and Mahoney’s recently published First Greek Course, which accompanies the reader. I hope the combination will be better than Athenaze, which doesn’t present readings that contain enough repetition of grammatical structures to fix them in the mind of the student, à la Ørberg, e.g., Iulius vir Romanus est. Aemilia femina Romana est. Marcus est puer Romanus. Quintus quoque puer Romanus est. Iulia est puella Romana. Marcus et Quintus non viri, sed pueri sunt. Viri sunt Iulius et Medus et Davus. Aemilia et Delia et Syra sunt feminae. Estne femina Iulia? Non femina, sed parva puella est Iulia. (I have omitted the macrons to save time typing.) This very brief excerpt (7 lines of the text) is taken from Lesson Two of Part One (Familia Romana of the Ørberg textbook. All of these characters are presented again and again in different contexts, often in a very humorous fashion, with accompanying helpful illustrations, so that the reader gets to know them well and looks forward to reading more of their adventures. And do you see the repetition of structures using a limited vocabulary that I am looking for in a Greek course? It’s certainly not in Athenaze or any other non-modern Greek textbook I’ve seen.
Has anyone ever seen a prescriptive grammar that uses this method to teach you how to read non-modern Greek? I love it! Lots of reading (121 lines of text in this lesson!) and helpful repetition of the grammatical structures and limited vocabulary (in this lesson, 35 words) that the lesson presents. I’m hoping that Rouse’s Greek Boy does as well. We’ll see. 
Now with regard to learning Greek and Latin in tandem – if your primary goal is to read materials in these languages, then do not waste your time learning how to translate from one language to the other or from Greek/Latin to English and vice-versa. If you wish to read well, you must move beyond the point of decoding. You must become so familiar with the grammatical patterns of the language that you know them almost as well as you do those of English (or your native language). By “familiarity” I mean subconscious recognition of the meaning of the patterns. To acquire this familiarity, I would limit the size of the vocabulary and stick with one author or style of writing until you know him or it well. I have ordered Fairy Tales in Latin: Fabulae Mirabiles to supplement the Ørberg materials. They are amusing and are at a level that I can handle fairly well. They will help me expand my vocabulary and improve my reading skills. So what if they are not in classical Latin. At this early point of my studies, I don’t care. I just want tons of material to read at my level. Read, read, and read – that is my motto. And prose, not poetry. KISS is the word, no? Eventually, I’ll get to the “greats,” but not now.
On the other hand, if you are primarily interested in the study of Greek and Latin as languages – in their phonology, morphology, syntax, etc. – and don’t care about learning to read but only about studying their grammar, then ignore what I have said.
And if you are still interested in developing the skills of translation, set that as a goal for later on, for after you have learned how to read Latin and Greek well. And start with Greek to Latin, not vice-versa. The highly flexible syntax and the nuanced use of particles in Greek make (elegant) translation into that language a terror for anyone who is just learning it. And you should pick a specific period to make it far easier – better even to pick a particular author’s grammatical and stylistic patterns – although even that is difficult if you choose the classical period, because the word order is so mobile. Translating into Koine would be easier, because the grammatical patterns were more fixed then.
Well, I hope this has helped somewhat.
All the best –
Gordon
