Six new rare-earth metal germanides with general formula RE2Al1-xGe2+x (RE = Tb-Tm, Lu; 0.13(2) <= x <= 0.37(2)) have been synthesized by direct fusion of the corresponding elements. Their structures have been established by single-crystal diffraction to crystallize with the orthorhombic space group Immm (no. 74), adopting the W2CoB2 structure type. The Al and Ge atoms are arranged in alternating planar layers, made of rhombic- and hexagonal-fragments. The rare-earth metal substructure consists of puckered four-connected nets. Electronic structure calculations support the coloring of the Ge and Al sites and account for the existence of a small homogeneity range. DC magnetization measurements for all specimens are also presented; based on the RKKY and mean-field theories for antiferromagnets, relationships between the chemical bonding and exchange interactions are discussed.