How do "scientific couples" (from different fields) find positions?
Many universities (like the one where my wife and I work) have dual-career hiring programs explicitly to address this issue. It's definitely worth asking—carefully—whether the universities you are considering have such a program.
Here's how our system works. Suppose Department X offers a faculty position to Partner A, and later department Y offers a faculty position to Partner B. Then Partner B's salary is paid 1/3 by department Y, 1/3 by department X, and 1/3 from a general campus fund.* (Note that X and Y may be the same department.)
So Department Y has a significant financial incentive to hire Partner B. On the other hand, Department X must be willing to pay extra for Partner A; in practice, however, once an faculty offer to A is actually on the table, most department chairs find it hard to refuse to help hire B.
This is why you have to be careful how and when you ask. It's illegal in the US to discriminate against a job candidate because they're married—we're not even allowed to ask—but it is completely legal to hire a cheaper candidate over a more expensive one. If department X already knows that you have a two-body problem, they also know that hiring you will be more expensive. The safest strategy is not to mention that your partner needs a position (or even that your partner is another academic) until an offer is on the table.
*When I originally posted this answer in 2012, this financial arrangement was de-facto permanent, but my university has recently refined its policies. As of June 2018, the joint funding arrangement is permanent (“recurring”) if Partner B has a tenure-track faculty position, and limited to three years otherwise.
This is a very difficult, and unfortunately common problem. It is dealt with in many ways, including all of the ones you mention. Solving the problem almost always involves a serious compromise by one or both parties. Couples can take many approaches:
Not compromise on their jobs: both take the best academic jobs they can find. This usually involves living apart, in different cities, sometimes for years. They end up with lots of frequent flyer miles.
One becomes an academic, the other leaves academia: this makes it much easier to live together, but might require a major sacrifice by one of the couple, if they had their heart set on an academic career.
Both compromise on placement quality: couples can commit to both finding academic jobs together. Since it is difficult to find two jobs at the same university, this often involves taking jobs at a lower ranked institution, or less desirable location than either could get on their own. Some universities specialize in recruiting couples: this can be a coup for the university, since they get two researchers who are both higher quality than they would normally be able to recruit.
A long (daily) commute for each person can represent an extremely successful outcome of type 1), or a less successful outcome of type 3). For example, it is possible (although grueling) for a couple to live in Princeton, and have one commute to Philadelphia and one commute to New York.
This is not to say that it is impossible to achieve perfect success: there are academic couples, both of whom are in the same department at the top university in their field. But this requires an extraordinary amount of both talent and luck.
I have not performed a literature survey, but the only solution that looks viable is to choose a large and well-connected city like London with plenty of scope for both fields.
It is very common in India to find faculty couples, especially in the IITs. It is advantageous for the university as they are, in a way, settling the couple and ensuring their long-term stay.