This is a blessed loss. Mate can be forced, but a draw can be achieved under the fifty-move rule.
To probe all KBBPvKRN positions, these tables and their transitive dependencies are also required:
KQBBvKRN · KRBBvKRN · KBBPvKN · KBBBvKRN · KRNvKBP · KBBNvKRN · KBBPvKR · KRNvKBB