Let $R$ be a Noetherian local ring, $I$ and $J$ be two ideals of $R$, and $M$ be an $R$-module. We study the relationship between the Bass numbers of $M$ and $H^{i}_{I,J}(M)$. It is shown that if $M$ is minimax and $\frak p\in {\rm W}(I, J)$, then $\mu^j(\frak p, H^{i}_{I,J}(M))$ is finite for all $i\in\Bbb N_0$ and $j\in\Bbb N_0$, whenever one of the following holds: (a) $I$ is a principal ideal of $R$, (b) $\dim_R M=1$, (c) $\dim R=1$, (d) $\dim_R M/{JM}=1$ (when $R$ is local and $M$ is finitely generated), (e) $\dim_R R/{J}=1$ (when $R$ is local).
