An apparatus and method for managing the receipt of communication traffic in the form of packets or other units. The apparatus includes a communication interface (e.g., a NIC, a TCA) coupled to one or more host computer systems. Through Direct Memory Access (DMA) operations, the interface reassembles payloads of received packets into host buffers based on their sequence numbers, without buffering them in the interface. Packet headers are separated from the payloads and passed to a host for protocol processing after the payload DMA is completed. Host buffers may be of virtually any size. For each communication connection, state information is maintained on the interface, which may identify an upper level protocol so that an upper level protocol header is passed to the host as part of the packet header, not as part of the payload. Protocol termination remains in the host.