Sorry but I'm not going to be able to investigate this since IBM's "My IBM registration" web page will not properly function and update the required information needed in order to download the "Trial download: IBM Notes 9.0". I have tried half a dozen times and it keep me in a loop by erasing all information inputted when I select the country. While I would have gladly spent time on the issue nonetheless I cannot be bothered to waste my time trying to resister to download and get nowhere when a the required registration will not function properly! 
Okay I tried again this morning and was caught up in the endless loop where it would wipe out all the registration information once I selected the country. Even if I selected the country first it would then immediately take me away from the current form and thus not allow me to properly register. It's a good thing I can be tenacious because yesterday I was a bit tired when I tried and while I didn't give up quickly nonetheless I'd had enough. This morning after seeing the same pattern repeated twice I then filled out the form and the last thing, once again, selected the country... however this time when I did, I immediately hit the Esc key. This stopped the Browser going forward to the next page and now with the country showing I was able to hit the Submit button at the bottom of the form finishing the process properly in spite of the obvious form programing error that exists when trying to register. So I'm now downloading the NOTES_9.0_WIN_EN_EVALUATION.exe file and will give it a go and see what I can find out about your issue.
Brian,
Two questions...
What I downloaded was the "NOTES_9.0_WIN_EN_EVALUATION.exe" file and noticed when installing it says it's the "IBM Notes 9.0 Social Edition", is that the same edition/version you have?
Highlighted in the screen shot below, did you install the "Notes Browser Plug-in", or did you just install the defaults or what?
Thanks,
Woody
The long story short is it worked for me as expected out of the box!
Okay, here is what I did...
In VMware Fusion > Preferences... > Default Applications, I have the "Open Web Pages (http, https) with: Safari" check box checked.
In the Windows 7 x64 Virtual Machine > Settings > Default Applications, I have the "Open your Windows files and web links using Mac applications" check box checked.
I downloaded the "NOTES_9.0_WIN_EN_EVALUATION.exe" file from ibm.com and installed it in a Windows 7 x64 Virtual Machine under VMware Fusion 5.0.3 under OS X Mountain Lion 10.8.3.
In Notes 9.0 I setup my Email Account as I was installing it and then in Notes 9.0 under File > Preferences...Web Browser, I have the radio button for "When clicking on a hyperlink in the client" set to "Use the browser I have set as the default for this operating system".
Next I downloaded my Email in Notes 9.0 and clicked on a hyperlink and it opened as expected in the Host OS in Safari. I also went back to VMware Fusion > Preferences... > Default Applications and changed the "Open Web Pages (http, https) with:" check box selection to Firefox and then clicked a hyperlink in Notes 9.0 in the Windows 7 x64 Virtual Machine and it too opened as expected in the Host OS in Firefox.
Also make sure In Windows 7 Control Panel that under the Internet Properties Programs Tab that it says "Internet Explorer is not currently the default web browser" and then under "Internet programs" on the same Tab click the "Set programs" button. Then scroll down to the bottom of the Default Programs > Set Associations window and make sure that HTTP and HTTPS are set to "Open URL in VMware Host" and "Default Host Application" as shown in the image below.
(Click image to enlarge.)
Woody,
My apologies for the delay in replying.
I went through this step by step. I had most everything set the way you indicated, EXCEPT for the last step.
In the Set Associations I had file types (http and https) set for Chrome, and the protocols (http and https) set for Chrome. Changed both to default host application and assumed that would work, but when I tried it I got an error message:
I have had to change the default sharing between the host OS (Mac) and Windows in order to accomplish something else. I know how to share folders in Windows with the Mac. I will have to hunt down where Lotus is saving this file and share that file.