Family law divorce; can I contest my husbands divorce papers and get my own in place for adultry

Really depends on your location, but as Divorce has generally changed to "No Blame" then this is no longer a valid reason.

You may always contest the other sides papers, Most places no longer ask for blame and they don't list. Judges don't really care why a divorce is happening.

Most people contest the division of property, spouse support or other issues.