A brake caliper assembly and an associated support structure comprises an external casing, a pair of brake pads connected and capable of being actuated by actuating means in order to impart braking force on the disc and comprising respective support elements and a layer of friction material. The support structure comprises a connecting arm that connects the caliper to the fork and a strut element capable of being subjected to compression or traction that extends between the support elements and a fixing portion provided on the fork and is connected to the support elements by means of a connecting element separate and independent from the external casing.