Claremont to Long Beach would be Metrolink to Red to Blue lines, presumably (there might be buses, but the trains are usually nicer.) I know Metrolink tickets also give you a free ride on the Red Line, so I assume the passes do too, but that still leaves you with the Blue Line to deal with. Metro Rail passes (which are, I believe, valid on various buses as well) go for $52 a month.

Er. Sorry. You hit my "disgorge random transit trivia" reflex.