  We continue the study of the $(a,b,m)$-copartition function
$\mathrm{cp}_{a,b,m}(n)$, which arose as a combinatorial generalization of
Andrews' partitions with even parts below odd parts. The generating function of
$\mathrm{cp}_{a,b,m}(n)$ has a nice representation as an infinite product. In
this paper, we focus on the parity of $\mathrm{cp}_{a,b,m}(n)$. As with the
ordinary partition function, it is difficult to show positive density of either
even or odd values of $\mathrm{cp}_{a,b,m}(n)$ for arbitrary $a, b$, and $m$.
However, we find specific cases of $a,b,m$ such that $\mathrm{cp}_{a,b,m}(n)$
is even with density 1. Additionally, we show that the sequence
$\{\mathrm{cp}_{a,m-a,m}(n)\}_{n=0}^\infty$ takes both even and odd values
infinitely often.
