Cost models are broadly used in query processing to drive the query optimization process, accurately predict the query execution time, schedule database query tasks, apply admission control and derive resource requirements to name a few applications. The main role of cost models is to produce the time needed to run the query on a specific machine. In a multi-cloud environment, this is insufficient in two aspects: firstly, the machines employed are not defined a-priori, and secondly, time estimates need to be complemented with monetary cost information, because both the economic cost and the performance are of primary importance. This work addresses these two shortcomings and aims to serve as the first proposal for a bi-objective query cost model that is suitable for queries executed over resources provided by potentially multiple cloud providers. Moreover, our approach is applicable to more generic data flow graphs, the execution plans of which do not necessarily comprise relational operators.