In many low- and middle-income countries, geographical accessibility continues to be a barrier to health care utilization. In this paper, we aim to better understand the full relationship between distance to providers and utilization of maternal delivery services. We address three methodological challenges: non-linear effects between distance and utilization; unobserved heterogeneity through non-random distance "assignment"; and heterogeneous effects of distance. Linking Malawi Demographic Health Survey household data to Service Provision Assessment facility data, we consider distance as a continuous treatment variable, estimating a Dose-Response Function based on generalized propensity scores, allowing exploration of non-linearities in the effect of an increment in distance at different distance exposures. Using an instrumental variables approach, we examine the potential for unobserved differences between women residing at different distances to health facilities. Our results suggest distance significantly reduces the probability of having a facility delivery, with evidence of non-linearities in the effect. The negative relationship is shown to be particularly strong for women with poor health knowledge and lower socio-economic status, with important implications for equity. We also find evidence of potential unobserved confounding, suggesting that methods that ignore such confounding may underestimate the effect of distance on the utilization of health services.