Hi,
I don't have experience with this, but I access the cache area of the browser sometimes which is possible to read, update, etc. An other approach can be using the Control-S to save the page or interacting with the file option of the browser and edit it afterwards, but I guess you want to read it frequently in which case you can look for new files in the cache area.
Perhaps you can even START the URL from COBOL and look in the cache area....
Tell us if you had success....