Families can pool their baggage allowances. Each service determines its travel uniform policies, and all but the Corps allow their personnel to travel in civilian clothes. But leave that torn tank-top at home, and be sensitive to accepted modes of dress in any country you're traveling to or through. It's a must to check well in advance of travel to find out what immigration or border clearance documents you'll need. In some cases service members can travel just on military I.D., but not always.
Many countries require passports, visas, medical documents or more, particularly for family members.