Can credit cards put a lien on your house for nonpayment if you and your spouse are separated?

Generally unsecured debt cannot put a lien on a primary residence. Doesn't matter whether you are separated or not.

the court may put a lien on your house. To answer your question about liens, liens from courts or the IRS (which are the only two real liens), will place lien on the house on record.

A few points here. First, most states exempt your personal residence from a lien for unsecured debt. Second, even if a lien is placed on the home it will only have a bearing when you try to sell the home. At that point the lien will need to be satisfied before the sale can be finalized. Finally, there is a third type of lien called a mechanics lien, that is placed on real property for payment for work done on that property.