I wouldn't add the whole members record, just a unique identifier from the Members table. That's all you really need and duplicating all the data in all the fields of Members in the event table is probably redundant here.
I think you also need an additional table for this so that one event can list many members and one member can attend many events:
Members::MemberID = EventRegistration::MemberID
Event::EventID = EventRegistration::EventID
A portal to EventRegistration on a members layout can list all events for which that member is registered. A portal to EventRegistration on the Event layout can list all members registered for that event. In both cases, fields from the third table can be added to the portal row to supply additional info. On the Members layout, for example, fields from the event table can be placed inside the portal row so you can see event names and dates for each event for which the member is registered.
Here's a demo file that matches up companies and contracts the same way you need to match members to events. Note how a pop up menu is set up to select a company to assign it to a contract or to slect a contract to assign it to a company.
http://www.4shared.com/file/PLhjErzu/Contracts_to_Companies.html (Click the Blue Download button)
Thanks a mil!! Philmod. It would be great if there were any good tutorials you know around.