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In a multi-channel marketing world, the purchase decision journey encounters many interactions (e.g., email, mobile notifications, display advertising, social media, and so on). These impressions have direct (main effects), as well as interactive influence on the final decision of the customer. To maximize conversions, a marketer needs to understand how each of these marketing efforts individually and collectively affect the customer's final decision. This insight will help her optimize the advertising budget over interacting marketing channels. This problem of interpreting the influence of various marketing channels to the customer's decision process is called marketing attribution. We propose a Bayesian model of marketing attribution that captures established modes of action of advertisements, including the direct effect of the ad, decay of the ad effect, interaction between ads, and customer heterogeneity. Our model allows us to incorporate information from customer's features and provides usable error bounds for parameters of interest, like the ad effect or the half-life of an ad. We apply our model on a real-world dataset and evaluate its performance against alternatives in simulations.