The following has been tested with Stunnel4 on Debian and Ubuntu.
To use an intermediate certificate with Stunnel you can simply combine the key, SSL certificate and intermediate certificate into a single file. Important is that you use the right order (key, certificate, intermediate certifcate) or it won’t work.
cat certificate.key certificate.pem intermediate.pem > stunnel.pem
Then specify the file in your stunnel config file, e.g. /etc/stunnel/stunnel.conf.
cert = /etc/stunnel/stunnel.pem
You do not need to add a key or CAfile value to your configuration file. You can check at http://certlogik.com/sslchecker/ if your certificate is working properly.