A disc brake caliper and hub bracket assembly for a disc brake of a vehicle, comprising: - at least one brake caliper, suitable for straddling a brake disc of a disc brake, said brake disc having a first braking surface and a second braking surface, opposite to said first braking surface, said disc brake defining an axial direction (X-X) coinciding with or parallel to the rotation axis of the brake disc, a radial direction (R-R) orthogonal to the axial direction (X-X) and a circumferential (C-10 C) or tangential direction (C-C) orthogonal both to the axial direction (X-X) and to the radial direction (R-R); - said brake caliper comprising a caliper body comprising a first elongated element, or vehicle side elongated element, suitable for facing said first braking surface of the brake disc directly or indirectly by means of at least a first brake pad, and a second elongated element, or wheel side elongated element, opposed to said vehicle side elongated element and suitable for facing said second braking surface of the brake disc directly or indirectly by means of at least a second brake pad; wherein said vehicle side elongated element of the caliper body comprises at least a first thrust means seat suitable for receiving a piston for exerting a thrust action on said at least a first brake pad; and wherein said wheel side elongated element of the caliper body comprises at least a second thrust means seat suitable for receiving a piston for exerting a thrust action on said at least a second brake pad; - said caliper body comprising at least one caliper bridge (10, 51) suitable for straddling the brake disc, said caliper bridge (10, 51) connecting said vehicle side elongated element and said wheel side elongated element; - said assembly further comprising a hub bracket suitable for providing a support for said brake caliper; said hub bracket comprising a hub bracket body connected to at least one portion of the vehicle side elongated element of the caliper body; - said hub bracket body comprising at least one coupling surface suitable for coupling to at least one bearing for supporting a wheel hub connectable to the brake disc and to a wheel of the vehicle; characterized in that said assembly comprises at least three connecting elements (57, 58, 59) which connect the hub bracket body to at least three separate portions of said vehicle side elongated element of the caliper body. - at least one brake caliper, suitable for straddling a brake disc of a disc brake, said brake disc having a first braking surface and a second braking surface, opposite to said first braking surface, said disc brake defining an axial direction (X-X) coinciding with or parallel to the rotation axis of the brake disc, a radial direction (R-R) orthogonal to the axial direction (X-X) and a circumferential (C-10 C) or tangential direction (C-C) orthogonal both to the axial direction (X-X) and to the radial direction (R-R); - said brake caliper comprising a caliper body comprising a first elongated element, or vehicle side elongated element, suitable for facing said first braking surface of the brake disc directly or indirectly by means of at least a first brake pad, and a second elongated element, or wheel side elongated element, opposed to said vehicle side elongated element and suitable for facing said second braking surface of the brake disc directly or indirectly by means of at least a second brake pad; wherein said vehicle side elongated element of the caliper body comprises at least a first thrust means seat suitable for receiving a piston for exerting a thrust action on said at least a first brake pad; and wherein said wheel side elongated element of the caliper body comprises at least a second thrust means seat suitable for receiving a piston for exerting a thrust action on said at least a second brake pad; - said caliper body comprising at least one caliper bridge (10, 51) suitable for straddling the brake disc, said caliper bridge (10, 51) connecting said vehicle side elongated element and said wheel side elongated element; - said assembly further comprising a hub bracket suitable for providing a support for said brake caliper; said hub bracket comprising a hub bracket body connected to at least one portion of the vehicle side elongated element of the caliper body; - said hub bracket body comprising at least one coupling surface suitable for coupling to at least one bearing for supporting a wheel hub connectable to the brake disc and to a wheel of the vehicle;