As @Brad notes, the WebPageElement type would be the closest match for something like a "webpage section". You could use the hasPart property to denote that they are parts of your WebPage.
But I think that it’s typically not useful to provide WebPageElement (or one of its child types) in the first place: don’t say something about how you structure your page, say something about the things you describe on your page.
So if you provide data about an organization, use Organization.  If you provide data about a service offered by an organization, use Service (→ provider Organization) etc.
Use the mainEntity property of your WebPage (or one if its more specific types) to link the primary item the page is about: 
- If the page is about a single organization, you could use:
ItemPage mainEntity Organization.  
If the page is about multiple organizations, you could add a list:
CollectionPage mainEntity ItemList
(and each Organization would be its own list item, added via itemListElement)
 
(By the way, even if Article would be appropriate in your case, you could still use WebPage in addition, so it’s not either-or. In that case, the mainEntity of the WebPage, or the more specific ItemPage, would be the Article item.)