We consider the distribution problem faced by a company that ships goods from a depot to multiple customers. This distribution is outsourced to multiple carriers offering different transportation rates and limited heterogeneous fleets of vehicles. Two shipping modes are used: in Less-Than-Truckload (LTL) mode, a shipment cost depends on its size and destination; in Full-Truckload (FTL) mode, routes should be designed for several fleets of heterogeneous vehicles, minimizing routing costs. This problem is formulated as a variant of a vehicle routing problem with time windows with private fleet and common carrier. To solve this problem, we use a matheuristic approach combining a Large neighborhood Search (LNS) metaheuristic with a Set Partitioning component. This algorithm embeds filtering strategies to efficiently integrate specific constraints in the LNS operators. We show that our method is competitive on less general problems benchmarks from the literature and we introduce new instances. We finally propose a case study arising from the French retail industry. We explore how the combination of FTL and LTL shipments can achieve substantial savings compared to pure FTL or LTL approaches.