RPL is an IPv6 routing protocol for low-power and lossy networks (LLNs) designed to meet the requirements of a wide range of LLN applications including smart grid AMIs, home and building automation, industrial and environmental monitoring, health care, wireless sensor networks, and the Internet of Things (IoT) in general with thousands and millions of nodes interconnected through multihop mesh networks. RPL constructs tree-like routing topology rooted at an LLN border router (LBR) and supports bidirectional IPv6 communication to and from the mesh devices by providing both upward and downward routing over the routing tree. In this article, we focus on the interoperability of downward routing and supporting its two modes of operations (MOPs) defined in the RPL standard (RFC 6550). Specifically, we show that there exists a serious connectivity problem in RPL protocol when two MOPs are mixed within a single network, even for standard-compliant implementations, which may result in network partitions. To address this problem, this article proposes DualMOP-RPL , an enhanced version of RPL, which supports nodes with different MOPs for downward routing to communicate gracefully in a single RPL network while preserving the high bidirectional data delivery performance. DualMOP-RPL allows multiple overlapping RPL networks in the same geographical regions to cooperate as a single densely connected network even if those networks are using different MOPs. This will not only improve the link qualities and routing performances of the networks but also allow for network migrations and alternate routing in the case of LBR failures. We evaluate DualMOP-RPL through extensive simulations and testbed experiments and show that our proposal eliminates all the problems we have identified.