Can custom post types display on blog page?

I am trying to configure a site whose blog will be for News and Events. I want to use the regular post type for news, but a custom post type (which would include dates and place) for events. Is there a way to set up a custom post type, set it for an Events category, but have both news & events show up in the blog page, in order of entry? The client doesn’t have frequent news or events, so I’d like to keep them together if possible, rather than having a separate page for each.