Here is an example of what I am talking about when I suggest an indoor aviary that is like a terrarium for birds:
Source:
Living Design, Inc.: Aviaries
There are some downsides to this style. Ventilation is a major concern for bird enclosures and birds can fly into transparent surfaces. Personally, I would recommend aviary mesh over plexi-glass. You lose out on aesthetics and mess-prevention, but gain in the health and safety columns.
For the naturalistic design elements, simpler is better. Try not to over-complicate your life by making things too cluttered and busy. It is harder to maintain and doesn't look that great. Be very aware of perch placement when planning the interior space and keep your floors as clear as possible to make it easier to clean up. Anything that goes inside the aviary needs to be bird-safe and easy to clean or replace, if soiled. Depending on your birds, fake plants might be an option to provide low maintenence greenery. Or you can look for non-toxic fast-growing plants that can be easily replaced if damaged or destroyed.
A jungle themed background, natural perches, and a few tall grasses or small palm trees could make for a pretty cool bird space.
Oh ... and keep in mind that your bird will appreciate open flight paths, stuff to chew, and multiple spots to land up high, so be sure that you provide all of those things in your naturalistic aviary design