This paper presents the results of an investigation on the bond behavior and stress-transfer mechanism of polyparaphenylene benzobisoxazole (PBO) fiber-reinforced cementitious matrix (FRCM) composites bonded to a concrete substrate using double-lap and single-lap shear tests. Results of double-lap shear tests with different composite bonded lengths and widths are presented and compared with those from single-lap shear tests previously reported by the authors. The idealized load response developed from single-lap shear tests is found to characterize the response of the composite in double-lap shear tests, although with a few key differences. With the double-lap shear test, load redistribution among the composite strips influences the post-peak response if debonding does not occur equally in both strips. Values of the ultimate (peak) stress determined using double-lap shear tests are generally consistent with, although slightly lower than, those determined by single-lap shear tests when the bonded length is longer than the effective bond length.