What should I do if I find that my husband is having an ambiguous message with another woman?

If you find out, you should show your attitude first. You can choose to ask and question, see the other person's reaction, then give a warning, set your bottom line and let the other person know what your attitude is. These certainly can't solve the problem immediately, but it is the beginning of solving the problem. Then, we will wait and see how the other party is doing and whether it can be corrected.