  We define counting and cocycle enhancement invariants of virtual knots using
parity biquandles. These invariants are determined by pairs consisting of a
biquandle 2-cocycle \phi^0 and a map \phi^1 with certain compatibility
conditions leading to one-variable or two-variable polynomial invariants of
virtual knots. We provide examples to show that the parity cocycle invariants
can distinguish virtual knots which are not distinguished by the corresponding
non-parity invariants.
