In my personal experience, by far the best bilingual material for someone approaching an L2, is L1 learning materials for L2 speakers. ¹ So, in your case, that’ll be ESL (English as a Second Language) materials for Japanese and Chinese speakers.

Why? Well, because, Grasshopper;

• There’s always way too much L2 material. ESL books for Japanese people contain more Japanese explanation and commentary than English.
• You realize that most grammar explanations are ex post facto realizations of a pattern that is best acquired unconsciously (and can only be realized by someone who has already acquired them unconsciously); you realize that they are unnecessary and almost always succeed in producing fear and confusion rather than comprehension.
• The English gives you a massive context cue: you always know what’s being talked about.
• You learn how to discuss the L2 in the L2 — how to explain words and ideas and grammar and stuff…with words: the reason this is valuable is because once you can explain words well, you can basically explain anything. Ever notice how accomplished linguists like Stevie Pinker and Noam van den Chomsky range so far outside of linguistics? Yeah, that’s why.
• The L2 (Japanese/Chinese) is almost always very natural, real, uncondescending, FUNBUN (for native by native). Sometimes there’s “translatese” (Japanese as it sounds translated from English), but this is mmm….relatively rare and not to be feared too badly.
• It’s a major confidence boost to realize that Japanese and Chinese L1 speakers are as depressed, brow-beaten, neurotic, erratic and generally sad about their English as you are about your Chinese/Japanese/whatever. And you already know English, so…you must be awesome in some way.
• It re-humanizes all people and languages, as you realize it’s not that Chinese or Japanese is hard (neither is), it’s just that the method is hard. There are no hard languages, only hard methods. There are no hard steaks, only blunt knives. Think of how ridiculous English spelling is. Yet we’re not about to change it and nor should we. All that needs changing is how it’s taught. Similarly, kanji doesn’t need “simplifying” or character reduction or any of that stupidity; the steak doesn’t need changing, only the knife.
• If it doesn’t suck (i.e. isn’t a school textbook), it’ll often cover very real, idiomatic, English-specific phrases and ideas that you’re gonna want to know how to express in the L2 anyhow.
• Conversely, if it does suck it’ll show you just how bad textbooks are and how stilted and unnatural and anachronistic the things they have you learn are.
  • People new to Japanese always think I’m exaggerating about how much JSL textbooks suck until I show them an ESL textbook. If you want to know how bad the Japanese in a typical JSL textbook is, just look at the English in an ESL textbook.
  • To be fair, not all ESL books that suck are textbooks, but most ESL textbooks, most language textbooks, do suck. I could draw you a Venn diagram, but then I’d have to upload it and that would be work and we can’t have that: I think it’s against my religion. ²

Finally, here are some links to the ESL material in question:

• Japanese: Cool English quotes translated into Japanese
• Chinese: Cool (very natural and useful) ESL example sentence page for Chinese speakers
• Japanese: CNN English Express
• Japanese: Eigo Journal
• English: AntiMoon — perhaps the ultimate example of this. AntiMoon is all technique, of course, but still.
• Warning (Discrecommendations) — now that I’ve shared some places to go ↑, here are some places not to go ↓:
  • One bilingual source that native Japanese speakers tell me doesn’t always have good (natural) Japanese examples is Space Alc.
  • Also, I notice that a lot (though by no means all…just a lot) of the bilingual examples at the Goo dictionary are “Englishese”/translatese — English-style Japanese — in that they use too many personal pronouns, far more than is natural in normal Japanese.
    • Tip of the hat to Jay Rubin and his “zero pronoun” explanation (theory?) of the Japanese language. In English, pronouns replace nouns. In Japanese, saying nothing, a total blank, (the zero pronoun) replaces pronouns replace nouns. Just like too many nouns sound dumb in English, too many pronouns sound weetordid in Japanese.
    • If you don’t want to throw out the baby with the bathwater, and there is plenty of baby at Goo, just ignore any and all (Goo) dictionary examples that contain a personal pronoun — “彼”, “彼女”, “私”, etc. — and you should be fine.