No, it is a one or the other. The SQL Server can’t require both. Windows authentication is much more secure than SQL Authentication as brute force attacks can’t be used against a Windows account when connecting to SQL Server as when using Windows Authentication the user must already be logged into the domain with a valid domain account. That then sends a token to the SQL Server, not the actual username and password.
You could probably accomplish this through a combination of encryption of the data and then application level decryption and security. So the domain credentials allow access to the app but then you can only get to the decrypted data by loging into the application.