I'm not a fluent right-to-left language speaker, but the general rule is, each chunk of other-direction text sits in the flow of the document where same-direction text would be, but oriented its own way within its own inner content.
The easiest way to find examples is to go to major Arabic or Hebrew websites that include a large volume of content about English / Western topics, therefore, plenty of snippets of correctly-formed opposite-direction text. These are more common and less frequently quirky than Western sites trying to accommodate Arabic/Hebrew/etc.
For example, here's the Arabic Wikipedia entry on the US sitcom Two And A Half Men: http://ar.wikipedia.org/wiki/Two_and_a_Half_Men You'll note that:
- The whole website is structured to work right-to-left, with elements placed on the opposite side to on the left-to-right sites and other consequent design and layout tweaks.
- English text is right-aligned to fit the layout (for example the URL and IMBD in the side box), and always placed in the flow of the document whereever a block of Arabic text would be.
- Anything wrapping around the chunk of English language text is as per the Arabic way. For example, punctuation, wrapper styling and interface elements. I can't find a clear example of the latter two, but if for some reason the IMBD text had an 'x' button to remove it, that would be placed where an Arabic reader would expect it (to the left of the text).
- Within the inner content of each individual other-language chunk, it's own language's rules apply. English text reads and is punctuated left-to-right as normal. (Don't even think of reversing Arabic text within the chunk of Arabic text so the letters or words run left-to-right! Not that anyone would do so deliberately, I hope, but just in case... Note also that non-Middle East edition versions of Creative Suite software do automatically reverse and mangle Arabic/Hebrew text like this, which is where blunders like that linked one originate from).
So as a general rule, not just for text direction,
- Wrappers and flow within the document will always use the master language (same as with language specific punctuation etc, e.g., Spanish language books I own that quote English language text in English always wrap the quotes in «Spanish style» quotation marks).
- Within the inner element of the other language content, its own rules apply (e.g. where those quotes themselves contain quotes, they are in the English style).
There's one possible exception where I'm not totally clear and where, from sites I've seen, there seems to be some inconsistency: the alignment within the text of other-language full-width multi-line block elements (e.g. block quotes).
Again I'm struggling to find good examples, but from memory I'm pretty sure that, on sites where other-language, other-direction blocks are rare exceptions in unusual articles (e.g. blogs, news sites where the original language wording is important to the story - rare cases), their inner text is aligned to match the master language and follow standard styles, breaking the above rule. Where they are a major part of the content of the site (e.g. a language learning site, or an English site about the Koran where most pages include many block quotes in Arabic), they more often have their own style which includes alignment as per their own language, as per the above rule.
Basically the rule if there is one seems to be a pragmatic one: are X language quotes a sufficiently important regular fixture on this site that they are a common type of content needing its own refined, perfected style, and where it's worth sacrificing a little consistency to maximise their readability and conventionality? Or maybe (perhaps more likely) it's just not really been thought about at all in the cases where it's an occasional anomaly, and so the style is just the default output. Just an observation.