Can you share more information on what you're attempting to do by connecting to remote server? If you're trying to copy files from or over to a remote server then there may be a better way to do it.
But to your question - the challenge I'm seeing is that there's a two step process when connecting to a remote server with credentials:
1. The first step is to connect to the actual server (using the following command: putty.exe -ssh username@my.company.com)
2. The second step is to enter the password when prompted: <password>
I'm not sure if there's a command that allows you to combine both steps into one. And it gets tricky, and possibly technically not doable, to keep or pass the ssh session between two steps. However, I did some googling on other tools and there's a tool called sshpass that allows to pass in the password using the -p flag.