There are a number of different factors to consider, and (broken record) each situation can be unique. The first place to start is the partners willingness to be included on an IRS tax or FBAR form. Do they feel their private financial information is being compromised? Then come the considerations: is eventual residence in the States planned shortly, does one partner contribute most of the income, which partner has investments, and is it advantageous for one partner only to have investments? Then comes the decision as to how to file, MFS or MFJ. As Barcrest says, most opt for MFS, but your case may be different.
On the house side, one may wish to consider the unspeakable; inheritance if one partner dies. How is the ownership of the house held? What are the HMRC implications, and the length of residence in the UK of the US partner?
No easy, straightforward answers.