The interval subdivision Int$(Δ)$ of a simplicial complex $Δ$ was introduced by Walker. We give the complete combinatorial description of the entries of the transformation matrices from the $f$- and $h$-vectors of $Δ$ to the $f$- and $h$-vectors of Int$(Δ)$. We show that if $Δ$ has non-negative $h$-vector then the $h$-polynomial of its interval subdivision has only real roots. As a consequence, we prove the Charney-Davis conjecture for Int$(Δ)$, if $Δ$ has non-negative reciprocal $h$-vector.