Concerns about polarization and hate speech on social media are widespread. Affective polarization, i.e., hostility among partisans, is crucial in this regard as it links political disagreements to hostile language online. However, only a few methods are available to measure how affectively polarized an online debate is, and the existing approaches do not investigate jointly two defining features of affective polarization: hostility and social distance. To address this methodological gap, we propose a network-based measure of affective polarization that combines both aspects – which allows them to be studied independently. We show that our measure accurately captures the relation between the level of disagreement and the hostility expressed towards others (affective component) and whom individuals choose to interact with or avoid (social distance component). Applying our measure to a large-scale Twitter data set on COVID-19, we find that affective polarization was low in February 2020 and increased to high levels as more users joined the Twitter discussion in the following months.