SQL Server doesn't send intermediate SSL certificates
To configure server side SSL for SQL Server, you will need to place the public CA certificate and private key in the certificate store of the service account running the database engine and place the certificate without the private key in the certificate store of the java VM initiating the connection. Then use SQL Server Configuration Manager to open the connection properties and set force encryption to yes and select the certificate to use, which would be the public CA certificate, for encrypting the connection. When an SSL connection is initiated, the SQL Server will present the certificate to the java VM and the java VM will find it in its store of trusted certificates and validate it directly against the CA without the need for walking the chain of trust for intermediate certificates. Since the server is on the Internet, it wouldn't hurt to configure ipsec so all traffic is encrypted. Also, It's good that you have a certificate from a public CA because if no certificate is configured, then SQL Server will used a self signed certificate and that configuration will leave you vulnerable to a man in the middle attack.