Mobile nodes are typically equipped with multiple radios and can connect to multiple radio access networks (e.g. WiFi, LTE and 5G). Consequently, it is important to design mechanisms that efficiently manage multiple network interfaces for aggregating the capacity, steering of traffic flows or switching flows among multiple interfaces. While such multi-access solutions have the potential to increase the overall traffic throughput and communication reliability, the variable latencies on different access links introduce packet delay variation which has negative effect on the application quality of service and user quality of experience. In this paper, we present a new IP-compatible multipath framework for heterogeneous access networks. The framework uses Multipath Datagram Congestion Control Protocol (MP-DCCP) - a set of extensions to regular DCCP - to enable a transport connection to operate across multiple access networks, simultaneously. We present the design of the new protocol framework and show simulation and experimental testbed results that (1) demonstrate the operation of the new framework, and (2) demonstrate the ability of our solution to manage significant packet delay variation caused by the asymmetry of network paths, by applying pluggable packet scheduling or reordering algorithms.