Well, I’m not totally sure I can troubleshoot your WebDAV connection with the information provided, but here’s some information and thoughts.
As you likely know, you connect to a WebDAV server the same way as you would to an SMB or AFP server. You connect via the proper URL, so as you would connect to your Synology NAS (let’s assume you named it SNAS) for smb via smb://SNAS.local/Share, you would connect via WebDAV to http://SNAS.local/Share. You would replace http with https if you are connected with an encrypted connection.
This is done from the Finder via the Connect to Server… item of the Go menu, or by typing ⌘K in the Finder and entering the server URL as noted.
Note that you would typically include your username (on the NAS) as part of the url, as http://username@SNAS.local/Share, and you might be using the IP address of the SNAS instead of its network name if that’s how you are referring to the NAS. Synology supports mDSN (Bonjour) so you can generally connect to SNAS.local. You can test that by ping’ing the NAS from a Terminal window, which if your husband is a Linux user, he would know how to do if you are uncertain.
Let’s assume that you have enabled WebDAV on the Synology, because you mentioned your husband can connect from his Linux box. Then you too should be able to connect. Note that on the Synology, you can enable services on a per-user basis, so make sure that whatever account you are using for the WebDAV login is enabled for that service. If you and your husband are using different accounts on the Synology, try making the WebDAV connection from your husband’s account on your NAS to see if that is the issue, or check the permissions on the Synology.
Another point is that the Synology by default does NOT use the standard WebDAV ports for the connection. Make sure you are connecting to the correct ports. By default, Synology uses port 5005 for WebDAV and 5006 for WebDAVS, so your full url then would have to become: http://username@SNAS.local:5005/Share or https://usernam@SNAS.local:5006/Share.
Hopefully this gets you on the right track; if not, perhaps post how your husband makes his connection and how you have your Synology set up and maybe I or someone else can help more.