Traffic in the Azure VMware Solution ExpressRoute circuit isn't metered in any way. Traffic from your ExpressRoute circuit connecting to your on-premises to Azure is charged according to ExpressRoute pricing plans.
Azure VMware Solution to vNet is through an internal ExpressRoute circuit and is free of cost within the same region as Azure VMware Solution. However, if the internal ExpressRoute circuit is connected cross-region, data transfer charges apply.
Azure VMware Solution to on-premises is done through vNet or ExpressRoute Global Reach (between the internal ExpressRoute and external ExpressRoute). It's still free provided the connection to vNet (mentioned above) or using ExpressRoute Global Reach is within the region where Azure VMware Solution is deployed.
For example:
If we connect a vNET in Azure West Europe to an Azure VMware Solution private cloud in West Europe, then there are no ExpressRoute charges other than the ExpressRoute gateway charges.
If we connect a vNET in Azure North Europe to an Azure VMware Solution private cloud in West Europe, then there are no ExpressRoute charges other than the ExpressRoute gateway charges.
If you connect an Azure VMware Solution private cloud in West Europe to an Azure VMware Solution private cloud in North Europe via Expressroute Global Reach you will NOT incur any ExpressRoute Global Reach data transfer (egress and ingress) charges. Please note that there will be charges when using an ExpressRoute gateway.