Abstract : In heterogeneous networks, devices communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available ones, each device might establish several connections. A connection may be established when the devices at its endpoints share at least one active interface. In this paper, we consider two fundamental optimization problems. In the first one (Maximum Flow in Multi-Interface Networks MFMI), we aim to establish the maximal bandwidth that can be guaranteed between two given nodes of the input network. In the second problem (Minimum-Cost Flow in Multi-Interface Networks MCFMI), we look for activating the cheapest set of interfaces among a network in order to guarantee a minimum bandwidth B of communication between two specified nodes. We show that MFMI is polynomially solvable while MCFMI is NP-hard even for a bounded number of different interfaces and bounded degree networks. Moreover, we provide polynomial approximation algorithms for MCFMI and exact algorithms for relevant sub-problems. Finally, we experimentally analyze the proposed approximation algorithm, showing that in practical cases it guarantees a low approximation ratio.