It depends. Ususally you will get a better result filing a joint return, but not always. If one spouse owns the house and has other sizeable itemized deductions, and the spouse with alimony payments has very little additional income, there might be a benefit in claiming married filing separately. However, it's not guaranteed. If one of the two spouses has significantly more income than the other spouse, that spouse would probably be in a higher tax bracket filing separately than if filing jointly. Another caveat is if you live in a community property state (LA, TX, NM, AZ, CA, NV, ID, WA, AK or WI). There is no tax benefit to filing separately in a community property state, and it is complicated to do so.
In addition, these same deductions (the house and the alimony) will both be deductible on a joint return as well. Plus, it is possible that the joint income, as indicated above, might be in a lower tax bracket on the combined amount than if separate.
The only way to know for certain is to prepare the returns both ways to compare (which does require setting up a "mock" return as Married Filing Separately). If you wish to do this, this FAQ gives instructions on how you would: https://ttlc.intuit.com/replies/4775330
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