In real recommendation scenarios, users often have different types of behaviors, such as clicking and buying. Existing research methods show that it is possible to capture the heterogeneous interests of users through different types of behaviors. However, most multi-behavior approaches have limitations in learning the relationship between different behaviors. In this paper, we propose a novel multilayer perceptron (MLP)-based heterogeneous sequential recommendation method, namely behavior-aware multilayer perceptron (BMLP). Specifically, it has two main modules, including a heterogeneous interest perception (HIP) module, which models behaviors at multiple granularities through behavior types and transition relationships, and a purchase intent perception (PIP) module, which adaptively fuses subsequences of auxiliary behaviors to capture users' purchase intent. Compared with mainstream sequence models, MLP is competitive in terms of accuracy and has unique advantages in simplicity and efficiency. Extensive experiments show that BMLP achieves significant improvement over state-of-the-art algorithms on four public datasets. In addition, its pure MLP architecture leads to a linear time complexity.