Assessing covariate balance for a propensity score model with interactions I am interested in determining the covariate balance of a PS model with high-order interaction terms. How can assess this? I have explored the use of standardized differences but I am running into problems because of the interaction terms in the model.

The form of the propensity score model has nothing to do with how you should assess balance. You should always assess balance on as many terms as possible, including interactions and other features of the covariate distribution. Different software make this easier or harder. If you are using cobalt to assess balance, you can just set int = TRUE in the call to bal.tab() to get standardized mean differences on all pairwise interactions. If you are using MatchIt, you can do the same in a call to summary(). If you want to test balance on specific interactions or higher-order terms, you can manually add them using the addl arguments to both functions.
There are some balance statistics that attempt to assess balance in the full joint covariate distributions (i.e., all possible interactions), like the L1 statistic and energy distance. These are good for comparing matching specifications but not necessarily for deciding whether a sample is "balanced" or not.
