In this paper, we propose a four-step decomposition of hybrid liabilities into a hedgeable part, an idiosyncratic part, a financial systematic part, and an actuarial systematic part. We generalize existing approaches for decomposing hybrid liabilities by incorporating dependence between financial and actuarial markets and allowing heterogeneity in policyholder-specific risks. Our model provides a market- and model-consistent valuation framework which we illustrate using a portfolio of with-profit pure endowment contracts.