Devices with multiple wireless interfaces are becoming increasingly popular. We envision that these devices will become the building block for future mesh networks, providing seamless connectivity across a range of heterogeneous devices. Although these devices typically implement frequency sharing, using either Direct Sequence Spread Spectrum (DSSS) or Frequency Hopping Spread Spectrum (FHSS), they may still interfere with one another. In this paper we provide a novel Radio Interference Avoidance (RIA) algorithm that solves the problem of interference between IEEE 802.11 and Bluetooth. We then extend this algorithm to other types of DSSS and FHSS combinations. Though the algorithm is limited to devices with both of these interfaces, this is a very common case. We analytically derive the expected value of the response time for RIA and run simulations to demonstrate its effectiveness. Our results indicate that RIA is able to eliminate interference with a very short response time. RIA also outperforms Adaptive Frequency Hopping, a solution proposed by the IEEE 802.15 Co-existence Working Group.