What you have is a many to many relationship. Any given member can be a member of more than one committee and any given committee lists more than one members. Adding a "join" table to match up members to committees is a better option than your check box group and will also allow you to pull up a committee record and assign members to it like you have requested:
Members::MemberID = Committee_Membership::MemberID
Committee::CommitteeID = Commitee_Membership::CommiteeID
With these tables and relationships, you can add a portal to committee_membership on a members layout to list that member's committees. A portal to committee_membership on a committees layout will list the members for that committee.
Here's how to set up your portal on the Committees layout. If you carefully follow the same pattern, you can set this up on the members layout as well:
Enable "Allow creation of records via this relationship" for Committee_Membership in the committee to Committee_membership relationship.
Place a portal to Committee_Membership on the Committees layout. Add the Commitee_Membership::CommitteeID field to the portal and format it as a drop down list or pop up menu of MemberID's from Members with the Member Names as field 2. In this value list, you can see the member name to select a member, but the memberID is what is entered in the field to link this record to a record in the member table. You can then add additional fields from the Member Table to this portal (such as the member name field) to provide additional info about each member on the committee.