A disc braking system (10) for a vehicle comprises a service caliper (12) suitable to be arranged astride a disc (14) rotating about an axis (16), said service caliper comprising at least one couple of service pads (18, 20). The system further comprises a floating parking caliper (30) suitable to be arranged astride the disc (14) and comprising a least one couple of parking pads (32, 34) housed in a floating structure (36) of the parking caliper. The floating structure comprises a side portion (38) and a bracket portion (40) extending from the side portion (38) in the axial direction to the disc (14). An individual mount structure (22) is provided which is suitable to be mounted on a fixed portion of the vehicle, and suitable to receive the couple of service pads (18, 20) and the floating parking caliper (30), which is slidably mounted thereon. Each parking pad (32, 34) is slidably inserted within a respective housing (48) of the mount structure (22) that is circumferentially defined by containment walls (50) being formed in the mount structure (22) and suitable to contain circumferentially opposed sides (52) of the parking pads (32, 34).