This paper uses Swiss firm-level panel data to estimate how complementarities among workers with different types of education affect firms' productivity. We subdivide workers by education into four groups: no post-secondary education, upper secondary vocational education and training (VET), tertiary professional education, and tertiary academic education. To account for possible endogeneity, we exploit within- firm variation and employ a recent structural estimation technique that uses intermediate inputs as a proxy for unobserved productivity shocks. Our results suggest that workers with an upper secondary VET education are complementary to workers with a tertiary academic education, while workers with no post-secondary education are complementary to workers with a tertiary professional education. In terms of firm characteristics, the results are surprisingly similar for low- and high-tech industries. Service industries, particularly modern ones, show both higher substitutability and higher complementarity, depending on the combination of workers. Large-size firms also show higher levels of substitutability and complementarity.