A density functional theory is developed for copolymers confined in a nanoslit on the basis of our previous work for homopolymers. The theory accurately captures the structural characteristics for diblock and alternating copolymers composed of hard-sphere or square-well segments. Satisfactory agreement is obtained between the theoretical predictions and simulation results in segment density profiles, segment fractions, and partition coefficients. Structures under confinement strongly depend on the substituent segment sizes for the hard-sphere copolymers and also on the segment-wall attractions for the square-well copolymers. Alternating copolymers are found to behave as homopolymers with effective segment size, and effective segment-segment and segment-wall interactions.