Yes, we 100% plan to include multiclassing. Some specialties give you a light touch of another class, but the full system allows you to integrate multiple classes. I see this as simply another area where players can choose how deep they want to go into a class or archetype.
1e and 2e had multiclassing. It was rare because it was fairly hard to actually pull off, barring a few places where it was essential- like 1e PHB bards and PHB Appendix psionics. 4e had similar multiclassing, but it was either Feat-based or you had a Hybrid Class character.
3.x and Star Wars, on the other hand, had stupidly beneficial multiclassing. There was no real benefit to taking a single class character (barring Prestige Classes, some of which can arguably be considered just a specialization of a basic class). And that's not touching some of the beardy cheese that CharOp would sometimes vomit forth. For example, a monk build that can choke out any spellcaster within a one-mile radius, in one round.
Now, because multiclassing was so stupidly beneficial, it also made character development and leveling really confusing. One mistake and your character would go from useful to useless. Some of this was because of math holes and tax feats; having to take an accuracy feat to still be able to hit monsters on less than a 17, for example. You also had the problem of Attack Bonus calculations because you had 1, 3/4, and 1/2- AB classes. Again, taking a level in the wrong class would totally destroy a combat build.
So with all that in mind, why does WotC keep trying to force multiclassing on us? I just don't see it being beneficial to 5e at all, compared to the damage it can inflict on game balance and design.