Let $X$ be a finite CW-complex of finite dimension. We can consider $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module ($i\geq 2$). My question is that is there any direct relation between $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module and $H_i (X)$'s as $\mathbb{Z}$-module? For example, if $\pi_i (X)$ is free as $\mathbb{Z}\pi_1 (X)$-module, then $H_i (Z)$ is a free $\mathbb{Z}$-module or conversely?

I know that the connection between homotopy groups and homology groups is given by the Hurewicz-Theorem. But I want a relation between $\pi_i (X)$'s as $\mathbb{Z}\pi_1 (X)$-module and $H_i (X)$'s as $\mathbb{Z}$-module particularly when there are free. Thanks in advance.