Is it possible to load balance between MPLS router/network and DIA router?

We have offices on a managed MPLS network. Two of the sites have there own Internet connection. One of the sites has a T1 MPLS and T1 Internet connection. The challenge is that on one site, some hosts download 10+Mb files from HQ through the MPLS network. The download takes about 10 minutes. How is it possible to load balance, whereby some packets are received through the Internet router and some packets from the MPLS router? The following is the topology.

Internet router, T1> ASA firewall> LAN> MPLS router, T1>MPLS network

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