If you are looking for one foursome and two threesomes each round then you could play something like this:
(7 8 6 5) (2 9 4) (3 10 1)
(2 8 10 7) (6 1 4) (5 3 9)
(9 10 6 8) (4 3 7) (5 1 2)
(5 2 6 3) (7 9 10) (1 4 8)
(9 6 1 7) (4 10 5) (2 8 3)
This gives all pairs of players together at least once and at most twice, but the distribution of players is uneven. Ideally you would want each player to be in two foursomes and three threesomes, however I don't believe it is possible to do this and have the pairwise balance at the same time.
Hope that helps.