screen doesn't come with any layouts predefined, so you need to roll your own. Here is what I've added to my ~/.screenrc :
# define layouts
layout new 'horizontal'
layout new 'vertical'
layout new 'main'
# bind control sequences for new layouts
bind V layout select 'vertical'
bind H layout select 'horizontal'
bind ' ' layout next # <- actually means Ctrl-a + Space
With this it's possible to switch layouts with Ctrl+a Space | V | H.
(Actually, all control sequences start with Ctrl+a by default, so I'll omit it from now on.)
This solution is not ideal - after starting a screen session you initially have to tediously focus on each 'region' (parts of a layout) with TAB, and attach a process (
man screen of all places insists on calling them 'windows' ) with n|p|0-9|Ctrl+c or a different method of your choice.
I imagine you'll want to detach instead of killing when possible.
... and this should hopefully cover your use case. Cheers!