As future small cell base stations (SCBSs) are set to be multi-mode capable (i.e., transmitting on both licensed and unlicensed bands), a cost-effective integration of both technologies coping with peak data demands is crucial. Using tools from reinforcement learning, a distributed cross-system traffic steering framework is proposed whereby SCBSs leverage WiFi, to autonomously optimize their long-term performance over the licensed spectrum band, as a function of the traffic load and users' heterogeneous Quality of Service (QoS) requirements. The proposed traffic steering solution is validated in a Long-Term Evolution (LTE) simulator augmented with WiFi hotspots. Remarkably, it is shown that the proposed cross-system learning-based approach outperforms several benchmark algorithms and traffic steering policies, with gains reaching up to 200% when using a traffic-aware scheduler as compared to the classical proportional fair (PF) scheduler.