In this paper, we propose a new routing protocol for home networks, called dependable routing protocol (DRP) that adapts to the changes in local topology within home networks environments. DRP is based on an effective selection of paths through which a packet must pass to reach the home unit. The selection, in such dynamic home networks, is made using dependable routing, i.e, in a way that maximizes the routes quality between the network nodes and the home unit while minimizing the Failure of Service (FoS). To minimize FoS, DRP maintains requirements on both the tolerable end-to-end delay (for time-sensitive routing) and the bit error rate (for reliable routing) within the network. To achieve this, we formulate the routing dependability problem mathematically as a constrained optimization problem. Specifically, analytical expressions for the route quality as well as the delay and bit error rate of a route in a home network scenario are derived. Numerical and simulation results show that the proposed approach gives optimal or near-optimal solutions and improves significantly the home network performance when compared to one prominent routing protocol: the Minimum Total Transmission Power Routing scheme, MTPR.