Thanks for writing in!
You can achieve this by having to add two containers to your bar. For the first container, you can insert your logo and for the second container, you can insert the navigation inline and a text element where in you can place the contact details and the button.
For each container, you will have to set the flex layout as column and for the element's flex layout, you may set it as column. Please create your custom header first and add your logo, menu and contact details. We can tweak the settings afterwards to copy the same layout as your example.
For more understanding on flex settings and how you maybe able to achieve what you want, please check out this knowledge base article: https://theme.co/apex/forum/t/pro-header-and-footer-builder-introduction/103, https://theme.co/apex/forum/t/using-flexbox/24851
Please let us know how it goes.