Recently, the concept of parity bias in integer partitions has been studied by several authors. We continue this study here, but for non-unitary partitions (namely, partitions with parts greater than $1$). We prove analogous results for these restricted partitions to those that have been obtained by Kim, Kim, and Lovejoy (2020) and Kim and Kim (2021). We also look at inequalities between two classes of partitions studied by Andrews (2019), where the parts are separated by parity (either all odd parts are smaller than all even parts or vice versa).