The *NON CODE* way of editing my pages went away!

Hello out there – and please understand when I say NOVICE, I mean NOVICE – so some of these terms mean nothing to me until I look them up and find their meaning.
I am the admin for a website that was originally created using Adobe Bridge or something that was far more complicated – the company (which consists of a board of directors that are all volunteer positions) hired one of their kids to transfer the data to ‘something user friendly’ and she selected WordPress. They did not pay for any of the upgraded themes, just the transfer of the data, so the website is basic black and white and since I am the Office Manager and therefore the only ‘true’ employee, I am responsible for updating the site and posting things, and I figured out how to do all of that fairly quickly, and I have played with it when I have had time to see what other nifty things we could do with it. But, here is my current issue which I need immediate assistance with:
I recently ran the software update because it had never been done, and now in the Editor field on each page where I normally have TWO screen options in which to make changes, one of which I believe is the CSS or what I refer to as the CODE looking page, and the other was the page that looked exactly like what we would see on the screen – including any photos that I had inserted, well, now the *easy* screen is gone and the only one remaining is the *code* page. It used to be that I would select the page I wanted to edit, and there was that screen with the page information that looked identical to what the viewer saw and then a tab that allowed me to switch back and forth to the *code* view. I have made some changes in this window, but it is time consuming, and I need the other one back. From what I have read, this is the Stylesheet, and I need to customize it? This is one of the Plug & Play options, correct? There is one other person who will be accessing the site and making some changes from time to time, so rather than have him do something disastrous like somehow delete the entire site, I would love to get this fixed!
Can anyone please help me?
Thank you, from a very beginner to hopefully a few people who are going to lead me into a better website!
Again, this is not what I do for a living.