Multi-behavioral sequential recommendation has recently attracted increasing attention. However, existing methods suffer from two major limitations. Firstly, user preferences and intents can be described in fine-grained detail from multiple perspectives; yet, these methods fail to capture their multi-aspect nature. Secondly, user behaviors may contain noises, and most existing methods could not effectively deal with noises. In this paper, we present an attentive recurrent model with multiple projections to capture Multi-Aspect preferences and INTents (MAINT in short). To extract multi-aspect preferences from target behaviors, we propose a multi-aspect projection mechanism for generating multiple preference representations from multiple aspects. To extract multi-aspect intents from multi-typed behaviors, we propose a behavior-enhanced LSTM and a multi-aspect refinement attention mechanism. The attention mechanism can filter out noises and generate multiple intent representations from different aspects. To adaptively fuse user preferences and intents, we propose a multi-aspect gated fusion mechanism. Extensive experiments conducted on real-world datasets have demonstrated the effectiveness of our model.