This study proposes a flight scheduling model with an added aircraft emission model to solve the schedule design, aircraft routing and cargo routing problems for a full-cargo airline, where aircraft emissions are explicitly part of the decision-making process. Our model considers both operational sustainability (maximisation of profit) and environmental sustainability (minimisation of CO2 emissions) in the objective function and can be used to identify trade-offs between the two potentially contrasting objectives. Aircraft emissions are modelled based on the aircraft type and load factor for each flight leg. Several experiments have been performed using 3 different sub-networks of a full-cargo airline as a reference, with instances of up to 8 airports, 3 aircraft and 25 cargo requests. The results show how different network characteristics and changes in cargo demand affect the profit decrease required to reduce emissions. On average, for a reduction of 25% of carbon emissions, profits in networks with short to medium-range flights decrease by roughly 14%. The expected loss of profit is larger and more inconsistent for networks that include long-range flights.