Every homeowner can seek to claim Principle Private Residence status on his/her main residence. The fact that a couple are married does not change this.
To do this successfully, HMRC would need to be satisfied that each individual was actually living in their own properties. There are no set of minimum rules as such but the sort of things HMRC will want to see to be convinced are:
registration on the Electoral Roll by both in their respective houses
utility bills each in respective owned name going to the two different houses
bank statements or other financial info going to the two separate houses
each being able to show the purchase of furniture for the respective house.
It is possible, but you can understand HMRC are likely to ask searching questions