First off, let's make sure we clear up one issue. If your spouse is itemizing deductions, you must also (or, rather, if you don't, you won't get any benefit - you won't get the standard deduction). See this IRS FAQ answer on itemizing when filing separately.
Second, the issue of whether your wife is permitted to deduct any of it is complex, and may suggest professional advice if it's worth it monetarily. The IRS has a few rules for deducting mortgage interest, all listed in publication 936, summarized here:
- You must itemize and use Form 1040
- The mortgage must be a secured debt, on a qualified home, in which you have an ownership interest
- You, or your spouse if filing jointly, must have taken out the loan
- You must have incurred the expense yourself (i.e., paid it)
- Additionally, there are some income, funds use, and mortgage balance requirements likely not relevant here.
I think the third point is a sticky point for you: you, and not her, are on the loan, and you're filing separately. The fourth point may be relevant also, depending on whether you're in a community property state or not (and depending on some other details).
As such, it seems likely that she may not deduct the mortgage interest.
But further, it sounds like you shouldn't either. If you truly don't have any other significant deductions, beyond presumably state income tax and property tax, it's possible that you may both be better off not itemizing.
For example, let's say your joint potential deductions are the interest ($6000), which is 4.5% on a $150k mortgage on a $180k home. Looking at property taxes, the median (25th state) is about 1% effective rate, so another $1800. Then your income tax - let's say you make $120000 jointly after the normal above-line deductions etc., and you live in a state like Missouri which seems to be about average according to the Tax Foundation with a 6% tax rate; simplifying things, you pay .06*120000 = $7200.
So your total deductions are $15000 ($6000+$7200+$1800). That's over the amount you'll get as the standard deduction ($12600), but not by that much. It's well possible you live in somewhere like Illinois (3.75%, so $4500; $12300 total) where it's better not to itemize.
Though this also assumes your incomes are more or less equivalent; of course, if she makes $90k and you make $30k, or the reverse, you have a different equation - but that can go both ways. If you're the one who would itemize the $6000 interest, and she has the higher income, for example, you may end up in a situation where you can deduct $10500 and her $4500, which would be bad for your overall taxes.
So - all in all, you are probably the one to do the interest deduction (but talk to a tax professional if you're unsure and it makes a big monetary difference), and consider if taking the standard deduction might be better for you two (and remember that you both have to make the same choice there).