Two mobile users communicate with a central decoder via two base stations. Communication between the mobile users and the base stations takes place over a Gaussian interference channel with constant channel gains or quasi-static fading. Instead, the base stations are connected to the central decoder through orthogonal finite-capacity links, whose connectivity is subject to random fluctuations. There is only receive-side channel state information, and hence the mobile users are unaware of the channel state and of the backhaul connectivity state, while the base stations know the fading coefficients but are uncertain about the backhaul links' state. The base stations are oblivious to the mobile users' codebooks and employ compress-and-forward to relay information to the central decoder. Lower bounds on average achievable throughput are obtained by proposing strategies that combine the broadcast coding approach and layered distributed compression techniques. Numerical results confirm the advantages of the proposed approach with respect to conventional non-robust strategies in both scenarios with and without fading.