Currently, Album Admins (parent members) are signed up to use the app version by default. You can, however, invite yourself to the browser version of your album as an Album Member. To do so, go to the Settings tab and tap "Invite Family". From there, you'll be able to send yourself an invitation to use the browser version by selecting a role under "Invite Album Members".
Please note that you'll only be able to see photos and videos shared with the whole family and you won't be able to upload from this account. If you're interested in uploading photos/videos from your computer, you can do so with FamilyAlbum Premium. To learn more, please visit FamilyAlbum Premium.