Crossplay Parties will arrive in the next update for Chivalry 2! In order to play in a party with someone on a different platform than you, you will need to add them as a friend via the new Invite Code system. On release, the Invite Code system and crossplay party functionality as a whole will be in Beta. so there may be a few bugs the team will need to fix. 

Read here for more info on how the feature works, and some minor issues present during the Beta period.