I think 18 months is the hardest time - it's much worse than the terrible two's!
Without knowing anymore about you guys, I would guess that you're probably a bit too lenient and your husband is a bit unreasonable. Does she instantly stop having a tantrum when he shouts at her? My guess is no. She probably feeds off of his frustration. For crying out loud, he yells at her and "freaks out" to get HER to stop yelling and freaking out? How long is it going to take for him to realize this is NEVER going to get her to stop throwing a fit?
Ignoring all of the tantrums is one strategy, but it's obviously not one your husband wants to get on board with. (I also don't necessarily agree that all fits should be ignored. Because it sends the message that throwing a fit is an acceptable way to handle strong emotions.) My advice is that the two of you need to sit down during a calm moment and hash out a plan of action that is acceptable to the two of you. Your husband obviously doesn't think ignoring bad behavior is acceptable and won't support you on this, so you both need to change your parenting styles (in my never-to-be-humble opinion!) If your husband is like most guys, he will probably appreciate and respect a specific plan of action. I would present him with one.
I would identify the specific behaviors and come up with a specific consequence: If she kicks the apartment floor, she is picked up and placed in her bed where she has to remain until she stops kicking the floor. (It'll take a lot of determination and repetition to get her to stay on the bed.) If she throws a toy in anger, the toy is taken away and placed in "toy time out." (You'll be amazed at how quickly she will stop throwing "favorite" toys.) If she pitches a fit in a restaurant, one of you must take her out of the restaurant, strap her into the car seat and sit with her for a specific period of time. Then the other parent comes out to sit in the car while you go back in to finish your dinner. (Be prepared to eat a few cold dinners alone, but do NOT just simply leave the restaurant and do NOT take her back into the restaurant - even when she calms down. She needs to see that her behavior has reasonable and predictable consequences and those consequences must be felt by her. It's no fun to sit in the car while Mommy and Daddy "enjoy" their meal inside the restaurant. Other tips for restaurant visits: Tell her what you expect of her before you enter the restaurant; Take something that will occupy her (we have a small bag of toys that ONLY gets opened in restaurants so the toys are especially interesting); Order her food immediately and ask the server to bring it out as soon as it's prepared.)
But, the two of you need to be calm, be calm, be calm while dealing with her. Small children are remarkably perceptive and don't necessarily distinguish between negative and positive attention. Toddlers are also all about power and control. She has the power to make Daddy freak out and shout. That puts her in control of Daddy now, doesn't it?
With regard to the downstairs neighbors: Buy or make them an apology card with a little handwritten note that explains the situation and apologizes for the noise. Let them know that you appreciate their patience while your daughter goes through this stage. I'd also include a little gift - perhaps a box of chocolates. I can't tell you how many conflicts (up to and including law suits) could have been avoided if someone just simply apologized and/or opened the lines of communication.