Federated learning (FL) operates based on model exchanges between the server and the clients, and it suffers from significant client-side computation and communication burden. Split federated learning (SFL) arises a promising solution by splitting the model into two parts, that are trained sequentially: the clients train the first part of the model (client-side model) and transmit it to the server that trains the second (server-side model). Existing SFL schemes though still exhibit long training delays and significant communication overhead, especially when clients of different computing capability participate. Thus, we propose Collaborative-Split Federated Learning~(C-SFL), a novel scheme that splits the model into three parts, namely the model parts trained at the computationally weak clients, the ones trained at the computationally strong clients, and the ones at the server. Unlike existing works, C-SFL enables parallel training and aggregation of model's parts at the clients and at the server, resulting in reduced training delays and commmunication overhead while improving the model's accuracy. Experiments verify the multiple gains of C-SFL against the existing schemes.