Blockchains have become increasingly important in recent years and have expanded their applicability to many domains beyond finance and cryptocurrencies. This adoption has particularly increased with the introduction of smart contracts, which are immutable, user-defined programs directly deployed on blockchain networks. However, many scenarios require business transactions to simultaneously access smart contracts on multiple, possibly heterogeneous blockchain networks while ensuring the atomicity and isolation of these transactions, which is not natively supported by current blockchain systems. Therefore, in this work, we introduce the Transactional Cross-Chain Smart Contract Invocation (TCCSCI) approach, which supports such distributed business transactions while ensuring their global atomicity and serializability. The approach introduces the concept of Resource Manager Smart Contracts (RMSCs), and 2PC for Blockchains (2PC4BC), a client-driven Atomic Commit Protocol (ACP) specialized for blockchain-based distributed transactions. We validate our approach using a prototypical implementation, evaluate its introduced overhead, and prove its correctness.