In the modern society, most networked critical infrastructures are coupled together and can be modeled as interconnected networks. Cascading failures caused by overload in interconnected networks are extremely complicated and still lack of corresponding researches. It is crucial to explore a systematic design and load management method for complex interconnected network. In this paper, a probabilistic heterogeneous capacity allocation model and a preventive load redistribution model are firstly proposed. Based on the novel models failure cascades in interconnected networks are studied in detail. Numerical simulations and analysis results show that robustness of interconnected network depends on the network topology, capacity allocation pattern and load management strategy. The novel models have guiding significance for the design and optimal management of robust interconnected infrastructure networks.