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Digital marketing campaigns generate increasingly complex, multi-channel customer journeys, yet conventional multi-touch attribution (MTA) approaches, including heuristic rules, Markov chain models, game-theoretic methods, and deep-learning approaches—struggle to represent the cumulative, delayed, and state-dependent effects that characterize customer behavior. This article proposes a non-Markovian Dynamic Bayesian Network (DBN) framework for MTA that represents customer journeys as sequences of observed touchpoints generated by latent behavioral (engagement/intent) states and extends the conventional first-order DBN by allowing the latent state at time tto depend on multiple preceding latent states. Channel-level attribution is computed through counterfactual removal-effect analysis on the resulting latent-state dynamics, enabling delayed and cumulative channel effects to be incorporated into attribution. The framework is positioned relative to heuristic, Markov-chain, Shapley-value, deep-learning, and graphical point-process approaches, and an experimental design combining synthetic non-Markovian simulations with real customer-journey data is proposed for evaluating attribution accuracy, predictive performance, and computational cost. An illustrative Monte Carlo simulation demonstrates the mechanism: the Email removal effect increases from 0.04207 under a first-order specification to 0.04863 under a second-order specification, representing an approximately 15.6% increase when cumulative repeated-exposure effects are introduced. The proposed framework provides an interpretable probabilistic alternative to black-box sequence models while extending the temporal depth of latent-state attribution beyond conventional first-order DBNs. Future empirical evaluation is required to establish its effectiveness, scalability, and generalizability across real-world customer journeys.