Providing JKS file to customer for consuming HTTPS service

I'm new to web development and encountered the following question at the company I work for: we have a SOAP web service with SSL and one our customers wants consume this web service.

They said they need a certificate to properly connect to our service, but when we have sent them the X.509 file with the public key, they said they need a JKS (Java KeyStore) file with both our public and private keys.

Is there any scenario where sending out such JKS file to someone is necessary? Is it really needed for consuming an SSL web service? Or is it a misunderstanding? We have tested our web service with SOAP UI and Fiddler, we didn't even need the public key certificate.