I think composite keys do have a place but each situation should be carefully considered. Two-field composite keys can avoid the need for adding a synthetic key field and hence this completely meaningless redundant data in multiple tables. Two natural fields used as a key is actually storing less redundant data than a synthetic key stored in two tables.
Moreover the storing of the "redundant" natural field in multiple tables can sometimes greatly simplify querying those tables. The synthetic key could require a join to another table to retreive a value that could be obtained directly from one of the natural fields without a join at all. This could be more of a pain and definitely far slower than using natural composite key.
However if either of the fields to be used in the composite is text of more than very few characters I would use the synthetic key because Access works with integers much faster than strings. Three fields as a composite key is really starting to become unwieldy.
If the relationships are set up correctly, the double join is automatically created by the query designer when the tables are added.