In-flight Internet connectivity is a necessity for aircraft passengers as well as aircraft systems. It is challenging to satisfy required quality of service (QoS) levels for flows within aircraft due to the large number of users and the highly varying air to ground (A2G) link capacities composed of satellite and direct air to ground communication (DA2GC). To represent service quality variations, we propose models for the generated traffic flows from aircraft and variations in A2G links. We present three different forwarding schemes based on priority, delay requirements and history of the dropped flows metrics. Forwarding schemes schedule the flows in real time by choosing either satellite or direct air to ground link depending on the delay and capacity requirements of flows to maximize the number of accepted flows with required QoS guarantees in terms of dropped packets and delay. Also, the effect of local caching is studied to fully satisfy the QoS requirement of flows in simulated flights. We implement the forwarding procedures and caching in ns-3 and test their performance in a current connectivity scenario of 100 Mbps capacity for both the satellite spot and ground base station in a one-hour flight. Our study shows that although the forwarding procedure based on a combination of priority and delay requirement has relatively better performance than the other schemes, which are based on priority only and weighted average of all metrics, in dropped packet percentage and delay, the current connectivity setup is not able to satisfy all QoS requirements. Furthermore, at least 0.9 cache hit rate is required to satisfy all flows for at least 50% of simulated flights.