One of the keys to being in a leadership position in any company is to promote the company and talk it up at every opportunity you get. Whether you're talking to your staff, to customers, or to people who know nothing about the company, there's no reason to bad-mouth the company that pays you. To do so is hypocritical and very unprofessional.
Sure, sometimes the company does things you may not agree with, or find even problematic, but venting frustrations about the company you work for to others, whether employees or peers, outsiders or family, sends entirely the wrong message. If there's an issue with a decision, you either embrace it and support it or don't and then leave. There's no middle ground for big issues, and little issues are not worth worrying about (and certainly not worth venting about). Being part of the executive team of any company means discussing issues and problems with your peers in the executive layer, and allow the natural progression of those ideas to come to fruition. But any issues with the executive layer need to be dealt with at the executive layer and not in public.
So how do you show your support for the company that gives you a great job and pays your bills? As an executive, there's lots of ways. First and foremost, believe in what the company does and how it does it, and talk it up and promote it at every opportunity. Whether you're motivating your team, helping a sales person with a tough customer, or simply explaining what your company does, being enthusiastic about it comes across as the biggest message you can send. If you are convinced, the person you're talking to will be more convinced, too. And customers especially will pick up on that: promote the product as if it was your best idea, and they will buy into it (literally and figuratively).
Know all you can about your company. Know the products. Know the mission statement. Know the financial situation. The more you know the more you can support and promote them. Get the information you need, don't hide in a corner, and you'll be seen as an active member of the executive. I like to know the company's history, how it got started, who was involved, and how they got to where they are. That helps you put the current situation in perspective and help understand the motivations of the founders.
But it goes beyond that. Any company I've worked for I have always bought shares in, when they are public. Whether anyone knows you have done so or not doesn't matter. The simple fact you are a stakeholder gives you an incentive. And if the management team knows you buy shares without being forced to, it sends the right message about your belief in the company. You don't have to put your life savings into the company, but holding some stock certainly sends the message you are optimistic.
Get involved with everything you can to support the company, too. If they do charity work, have an office committee, run training courses, or whatever the activity, get involved and show your support. I've always asked to be on things like office committees, believing a little executive-level influence will help them accomplish what they want, as well as showing that you're not above everyone else. Sports teams in the company are a great way to participate too: everyone is equal on the field or court, and it's not just fun but good exercise. Certainly showing you're a team player helps your standing with employees, too.
There's a lot you can do to support your employer. Get involved and stay involved. Talk it up. Be their cheerleader. You'll reap the rewards in many ways. But absolutely, under no circumstances, bad mouth the company, especially in public or to others in the company. To do so is just bad form in every way.