A Gaussian interference channel (IC) aided by a half-duplex relay is considered, in which the relay receives and transmits in an orthogonal band with respect to the IC. The system thus consists of two parallel channels, the IC and the channel over which the relay is active, which is referred to as Out-of-Band Relay Channel (OBRC). The OBRC is operated by separating a multiple access phase from the sources to the relay and a broadcast phase from the relay to the destinations. Conditions under which the optimal operation, in terms of the sum-capacity, entails either signal relaying and/or interference forwarding by the relay are identified. These conditions also assess the optimality of either separable or non-separable transmission over the IC and OBRC. Specifically, the optimality of signal relaying and separable coding is established for scenarios where the relay-to-destination channels set the performance bottleneck with respect to the source-to-relay channels on the OBRC. Optimality of interference forwarding and non-separable operation is also established in special cases.