This paper proposes a relay-connecting coverage problem in heterogeneous wireless sensor networks. The aim is to find a minimum relay-connecting set cover (MRCSC) that satisfies the following: 1) Active nodes in a set cover fully sense the task area. Motivated by triangular lattice placement with asymptotic priority, a rule is designed to restrict abnormal spreading and to form an approximate triangular lattice; 2) Active nodes are relay-connecting, which means any active node connects at least one super node with a given success data forwarding rate. Relay-connecting prevents the interference of nodes that have low success data forwarding rates that are caused by the long path nodes take to the sink and radio channel. Theoretical analysis simulations show that the coverage of MRCSC nearly reaches that of OGCD, but relay-connectivity of active nodes is strongly reinforced with a limited number of additional nodes.