Causal models consisting of structural equations have proved a powerful formalism for approaching theoretical and applied questions on causal reasoning. The standard framework assumes that all variables that appear in a causal model must represent properties or events that are metaphysically independent, with no dependencies more intimate than causal relations, such as conceptual, constitutive, or other ontological dependencies. However, there are important contexts that call for lifting this restriction, such as the debate over high-level causation in philosophy and the task of causal representation learning in artificial intelligence. This paper proposes a natural generalization of structural causal models to accommodate (asymmetric) ontological dependence and provides an interpretation of causal counterfactuals based on such models. We discuss several implications of this generalization and present an axiomatization of the resulting counterfactual logic.