Summary: Let \(P = (\{1, 2, \ldots, n\},\leq )\) be a poset, let \(V_1 , V_2 , \ldots, V_n\) be a family of finite-dimensional spaces over a finite field \(\mathbb F_q\) and let \[ V = V_1\oplus V_2 \oplus \ldots \oplus V_n. \] In this paper we endow \(V\) with a poset metric such that the \(P\)-weight is constant on the non-null vectors of a component \(V_i\), extending both the poset metric introduced by Brualdi et al. and the metric for linear error-block codes introduced by Feng et al.. We classify all poset block structures which admit the extended binary Hamming code \([8; 4; 4]\) to be a one-perfect poset block code, and present poset block structures that turn other extended Hamming codes and the extended Golay code \([24; 12; 8]\) into perfect codes. We also give a complete description of the groups of linear isometries of these metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset metric spaces. In particular, we obtain the group of linear isometries of the error-block metric spaces.