Cloud computing provides on-demand access to affordable hardware (e.g., multi-core CPUs, GPUs, disks, and networking equipment) and software (e.g., databases, application servers and data processing frameworks) platforms with features such as elasticity, pay-per-use, low upfront investment and low time to market. This has led to the proliferation of business critical applications that leverage various cloud platforms. Such applications hosted on single/multiple cloud provider platforms have diverse characteristics requiring extensive monitoring and benchmarking mechanisms to ensure run-time Quality of Service (QoS) (e.g., latency and throughput). This paper proposes, develops and validates CLAMBS-Cross-Layer Multi-Cloud Application Monitoring and Benchmarking as-a-Service for efficient QoS monitoring and benchmarking of cloud applications hosted on multi-clouds environments. The major highlight of CLAMBS is its capability of monitoring and benchmarking individual application components such as databases and web servers, distributed across cloud layers (*-aaS), spread among multiple cloud providers. We validate CLAMBS using prototype implementation and extensive experimentation and show that CLAMBS efficiently monitors and benchmarks application components on multi-cloud platforms including Amazon EC2 and Microsoft Azure.